kuahji
Sep21-08, 06:55 PM
Write a in the form a=a_{Y}T+a_{N}N without finding T and N at the given t-value.
r=t\widehat{i}+3t^{2}\widehat{j}+t^{2}/2\widehat{k} , t=2
The first thing I did was to find the first derivative. Which turned out to be i+6tj+tk
Then I found the length \sqrt{1+37t^{2}}
Then I took the derivative of that to find a_{T} 37t/\sqrt{37t^{2}+1}
So my question really is, for a_{N} do I really have to plug that mess into \sqrt{|a|^{2}-a_{T}^{2}}
r=t\widehat{i}+3t^{2}\widehat{j}+t^{2}/2\widehat{k} , t=2
The first thing I did was to find the first derivative. Which turned out to be i+6tj+tk
Then I found the length \sqrt{1+37t^{2}}
Then I took the derivative of that to find a_{T} 37t/\sqrt{37t^{2}+1}
So my question really is, for a_{N} do I really have to plug that mess into \sqrt{|a|^{2}-a_{T}^{2}}